Time-variant system reliability analysis method for a small failure probability problem

Highlights: • A new single-loop strategy for time-variant system reliability analysis is proposed. • The multiple response Gaussian process is adopted to depict the correlation between time-variant limit state functions. • The subset simulation is introduced into the proposed single-loop strategy to estimate the small failure probability. • The updated strategy and stopping criterion for the proposed single-loop time-variant reliability analysis are provided. This paper proposes a time-variant system reliability analysis method by combining multiple response Gaussian process (MRGP) and subset simulation (SS) to solve the small failure probability problem. One common method for time-variant reliability analysis is based on the double-loop procedure where the inner loop is the optimization for extreme values and the outer loop is extreme-value-based reliability analysis. In this paper, a new single-loop strategy is firstly proposed to decouple the double-loop procedure by using the best value in current initial samples to approximate the extreme value, thus the extremal optimization in inner loop can be avoided. Then the MRGP model is used to construct the surrogate model of extreme value response surface for time-variant system reliability analysis based on the approximated extremums. Meanwhile, the Kriging model is also constructed based on the initial samples to assist in searching the new sample point. Furthermore, for selecting the new point that resides as close to the extreme value response surface as possible from the Monte Carlo simulation (MCS) sample pool, three learning functions (U-function, EFF-function and H-function) are respectively used to find the new random variable sample point based on the MRGP model and the expected improvement (EI) function is used to find the new time sample point based on the Kriging model. Finally, for reducing the size of candidate sample pool and the computing burden, the SS method is combined with the MRGP model to deal with the small failure probability problem. The effectiveness of the proposed method is also demonstrated by several examples.